By Raymond S. Nickerson
Inability to imagine probabilistically makes one liable to numerous irrational fears and prone to scams designed to use probabilistic naiveté, impairs determination making less than uncertainty, enables the misinterpretation of statistical info, and precludes severe evaluate of probability claims. Cognition and likelihood provides an summary of the knowledge had to keep away from such pitfalls and to evaluate and reply to probabilistic events in a rational means. Dr. Nickerson investigates such questions as how strong people are at pondering probabilistically and the way constant their reasoning below uncertainty is with ideas of mathematical information and likelihood conception. He experiences proof that has been produced in researchers' makes an attempt to enquire those and related sorts of questions. Seven conceptual chapters handle such themes as chance, likelihood, randomness, coincidences, inverse likelihood, paradoxes, dilemmas, and data. the remainder 5 chapters concentrate on empirical reports of individuals' skills and obstacles as probabilistic thinkers. subject matters contain estimation and prediction, notion of covariation, selection less than uncertainty, and other people as intuitive probabilists.
Cognition and likelihood is meant to entice researchers and scholars within the components of chance, records, psychology, enterprise, economics, determination conception, and social dilemmas.
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Additional info for Cognition and Chance: The Psychology of Probabilistic Reasoning
The claim that the length and frequency of streaks of successful shots do not exceed the laws of chance is based on an analysis of shooting records of professional players by Gilovich et al. (1985). Gilovich et al. (1985) note that they do not attempt in their analysis to capture all that people might mean by “the hot hand” or “streak shooting,” but they argue that the common use of the terms implies that the sequences of hits and misses of basketball shots should differ from sequences of heads and tails produced in coin tossing in two ways: (a) the probability of a hit should be greater following a hit than following a miss, and (b) the number of streaks of successive hits should be greater than the number produced by a chance process with a constant hit rate.
Still, there seems to be no way to specify the new list of numbers Randomness 30 that is shorter than the sequence itself…. Hence, according to Kolmogorov’s definition, the sequence is random, despite the element of design in its generation, (p. 15) (Devlin’s treatment of equal representation as evidence of design may seem contrary to the treatment a few pages back of equal representation as evidence of randomness. But note that the earlier reference said approximately equal percentages after a large number of selections.
When does it beg a causal explanation? These are difficult questions, and challenges to the statistical decision making, a subject to which we return in chapter 10. It suffices to note here that apparent structure can happen by chance and apparent structure will happen by chance. Search for structure among outputs of a random process is bound to succeed. It does not follow, however, that all apparent structure should be dismissed as effects of chance. How Does One Prove a Probability to Be Wrong?